Problem: William is 4 times as old as Ben. Twelve years ago, William was 7 times as old as Ben. How old is William now?
Solution: We can use the given information to write down two equations that describe the ages of William and Ben. Let William's current age be $w$ and Ben's current age be $b$ The information in the first sentence can be expressed in the following equation: $w = 4b$ Twelve years ago, William was $w - 12$ years old, and Ben was $b - 12$ years old. The information in the second sentence can be expressed in the following equation: $w - 12 = 7(b - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to solve our first equation for $b$ and substitute it into our second equation. Solving our first equation for $b$ , we get: $b = w / 4$ . Substituting this into our second equation, we get: $w - 12 = 7($ $(w / 4)$ $- 12)$ which combines the information about $w$ from both of our original equations. Simplifying the right side of this equation, we get: $w - 12 = \dfrac{7}{4} w - 84$ Solving for $w$ , we get: $\dfrac{3}{4} w = 72$ $w = \dfrac{4}{3} \cdot 72 = 96$.